GRE Math Techniques – The Power of Estimation

Many of us, when we first see a math question, hone in on it with laser-like focus. We make sure we read all the relevant parts, and then work out a solution to the problem. Only then do we look at the answers.

There is nothing inherently wrong with approaching a math problem this way; often times, it yields the right answer. But the GRE is a timed test, and solving for the exact answer to every problem is only going to eat up time.

Is there another—almost magical—way of solving a GRE math problem? Well, yes, depending on how you define magic. Once I show you the following technique, and you are able to apply it, you may very well think it magical.

First off, try the following problem.

1. If Machine X can make 40 widgets in 8 minutes, how many widgets can it make in 1 hour?

(A) 90

(B) 180

(C) 240

(D) 300

(E) 320

Okay, did you find yourself reading the question, setting up a proportion and then solving for the unknown? If so, no worries. You are simply taking the long approach.

Let’s instead look at the answer choices as soon as we’ve finished reading the question. There is quite a spread between the answer choices, as is often the case with GRE math problems. The range is 90 to 320. If the machine is already pumping up 40 widgets in 8 minutes, it’s definitely going to make more than 90 in 60 minutes. In fact, 60 minutes is almost 8 times as great as 8 minutes. Therefore the machine is going to make almost 8 times more than 40. Well, 8 x 40 = 320 (E), so that’s too big. So, which is number is slightly smaller? (D) 300. And there’s your answer.

This technique is called estimation. Learning to apply it accurately will save you time. It will also help with those more difficult questions, on which you really need your laser-like focus.

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About Chris Lele

Chris Lele is the GRE and SAT Curriculum Manager (and vocabulary wizard) at Magoosh Online Test Prep. In his time at Magoosh, he has inspired countless students across the globe, turning what is otherwise a daunting experience into an opportunity for learning, growth, and fun. Some of his students have even gone on to get near perfect scores. Chris is also very popular on the internet. His GRE channel on YouTube has over 10 million views.
You can read Chris's awesome blog posts on the Magoosh GRE blog and High School blog!
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Great! You took the proportion approach that Chris describes right after the question, which is absolutely correct. However, one of the purposes of this blog post is to try to get you to think outside the box and solve this question in a different way! This is a relatively simple question by GRE standards and while you may find some similar ones on your actual test, they won’t be very common 🙂

Well, the problem: “What is 26.3% of $7,935” can indeed be, at least solved approximately without using a calculator at all. 26.3 % is quite closer to, but a little bit more than, 25%. 25% is, however, exactly one-fourth of any quantity. Now let’s look at the amount 7,935. Without using a calculator, we can approximately say that 1/4th of this amount is somewhere near 2,000, but slightly less than 2,000. Now, let’s look at the percentile 26.3%. It is, as I mentioned before, slightly more than 25%. That means, the 26.3% of 7,935 must be slightly more than the quarter of it, which is somewhere around 2,000. Now, let’s look for a quantity around 2,000 in the options. Bingo! We found $2086.91. So, that should be that answer.

See, in this total calculation, it took me only about 1 minute, and I’ve done the entire math without using any calculator at all. It’s actually awesome and more fun than using calculator, and in reality, it is way faster than using the on-screen calculator. 🙂

The way I did this problem in my head is I divided 40 by 8, got 5, so that meant that 5 widgets are made in 1 minute, and there are 60 minutes in a hour, so I multiplied 5 and 60 to get 300, is it ok to do the problem like that in my head or should I concentrate more on doing it through estimation?

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